Depends on their use case specifically
and their requirements etc, someone on LinkedIn mentioned to me last week something along the lines of "if you're going to build a CDN you have to use cloud", which is a line of BS, they thought pretty much all CDNs used public cloud (and I have no doubt many/most/all CDNs probably have some aspect of public cloud usage). Global, real time mass comms platform as CDNs are as well, all of the major ones and probably most/all of the minor ones use their own infrastructure for their edge. Not only for cost reasons but also (more important for them) routing/traffic control reasons (less important for an app like Signal).
You can see pretty easily whether or not a CDN node(the most important part of a CDN) is using a public cloud or their own stuff by just looking at it's IP, if the WHOIS info for the IP reveals a public cloud provider then that is clearly cloud, if it does not then most likely it is their own infrastructure.
I know for example when Snapchat went public, here on el reg there was an article (https://www.theregister.com/2017/02/03/snap_files_for_ipo/), where Snapchat said they had commited to spending $400 MILLION PER YEAR to Google for their cloud stuff. Sorry it's going to be hard to convince me that they can't build their own global network for a lot less than $400M per year... Snapchat is in a similar model as Signal I think ... ? (never having used Snapchat though I do use signal).
To me, one of the best (on paper) use cases for public cloud is you have to go from say ~100 CPU cores to 5,000 CPU cores for max of 2 hours per day (averaged over a month, so say max of 60 hours per month). Building infrastructure for ~60 hours of month of usage probably doesn't make sense (though I haven't run the numbers specifically). Another really good use case for public cloud is one off things, such as I think I have seen at least one article here on el reg about some group doing some kind of HPC test on cloud where they spun up a few thousand servers or something to do one test, then spun them down(never to be needed again). Obviously such situations are few and far between.
(Again on LinkedIn) there was a cluless tech leader dude from State Farm who wrote a dumb post saying everyone should use cloud, at their scale they want their business not to be focused on computers etc (typical outsourcing BS), anyway found it kind of ironic more recently another person posted about how Geico (same industry as State Farm, insurance) spent a decade moving into public cloud spending $300M/year, only to find out(why did it take a decade to find out?) that it costed them 2.5X more, and now they have reversed course.
But most anything with a real steady state load in 95%+ of use cases doesn't make sense to have on public cloud.
THAT SAID - if you are happy with overpaying your public cloud provider and don't care about the costs you are just a happy customer that is fine, continue to use them, just don't pretend that you are saving any money.
IaaS is broken by design, something I first wrote about 15 years ago and posted a link here on El reg, here is the link again
http://www.techopsguys.com/2010/10/06/amazon-ec2-not-your-fathers-enterprise-cloud/
Some back story to that, at the time the CEO of the company I was at was/is the sister of the head of Amazon cloud (now is the CEO of Amazon). I actually met with him and his chief scientist back in 2010 to complain about their bad service and he spent a bunch of time apologizing for it. But that's not the real story. The real story is even though I sent that link to my boss on that same day, he read it, and he thought it was a well thought out balanced post, someone over at Amazon got into a hissy fit and that came down on my employer(was before noon on the same day as I posted it) whom then gave me legal threats to take the post down(BS reasons), they threatened me again when I left the company (and triggered a mass exodus from the tech team, about a dozen came to the next company). I complied and hid the post for a few years, they eventually went out of business and I put it back up online about a decade ago.
I've started to think I will refer to these people (like that State Farm person above), as members of "Cult of the Cloud". (for whatever reason I came up with that sort of named similarly as "Cult of the Dead Cow"), where they can be faced with so many different facts and figures and they are so brainwashed that they just can't believe their eyes/ears (similar to "MAGA" folks). Same sort of thing applies to so many folks pushing Kubernetes as well(and "IaC" to a lesser extent). All complicated coping means to try to tame "the cloud". Make it simpler, don't use it. (I happily admit there are use cases for all of these things they just don't apply to everyone(don't apply to most really), and many of these folks think these things should apply to everyone).
The post is still valid today, as the flawed design of IaaS remains unchanged.
I moved my last org out of AWS in early 2012 with a 7 month ROI, and followed with a decade of flawless operation.